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Contents
 
Primes  k · 2n + 1  List of primes for k < 300
List of primes for 300 < k < 600
List of primes for 600 < k < 900
List of primes for 900 < k < 1200
Frequencies (updated)
History (new)
Fermat numbers Standard factoring status  
Factors of generalized Fermat numbers  
GFN03 factoring status
GFN05 factoring status  
GFN06 factoring status
GFN07 factoring status
GFN10 factoring status  
GFN11 factoring status  
GFN12 factoring status
Search limits and reservations
Primes  k · 2n − 1  List of primes for k < 300
The Sierpiński problem   Definition and status  
The Riesel problem Definition and status  
Cullen primes Definition and status  
Woodall primes Definition and status  



Last modified (and updated) December 31, 2022.

Lists of primes  k · 2n + 1  and  k · 2n − 1  updated:
all currently known primes included.

GFNfacs.html now contains 8383 "new" divisibilities,
340  of which were found during this year.  
2021 had been a particularly productive year for GFN
factors: 745 divisibilities found!  
Number of divisibilities discovered in previous years:
615 (2020), 41 (2019), 27 (2018), 18 (2017) 46 (2016),
79 (2015), 136 (2014), 213 (2013), 457 (2012).

November 27, 2022:
Candidate of Riesel Problem eliminated.

July 25, 2022:
New largest known factor of a Generalized Fermat
number found:
 7 · 220267500 + 1  divides  GF(20267499,12). 

March 8, 2022:
A second long-term omission was detected in the list
of primes k · 2n + 1 : the prime 281 · 22051865 + 1 had
to be added.

November 25, 2021:
Candidate of Extended Sierpinski Problem eliminated.

November 24, 2021:
New factor of Fermat number F(1379).

August 11, 2021:
New factor of Fermat number F(66643).

June 29, 2021:
First factor of GF(9,11) found, a P52 prime.

May 2021:
A long-term omission was detected in the list of primes
k · 2n + 1 : the prime 879 · 2110075 + 1 had to be added.

Five Riesel problem candidates eliminated within less
than six months:

k = 146561 (16 Nov 2020), k = 9221 (07 Feb 2021),
k = 2293 (13 Feb 2021), k = 192971 (07 Mar 2021),
k = 206039 (26 Apr 2021).

March 27, 2021:
6896-digit final factor of xGF(13,7,5) proven prime.

March 12, 2021:
First factor of GF(14,10) found, a P37 prime.

March 1st, 2021:
New factor of Fermat number F(40).

December 31, 2020:
In 2020, 612 GFN divisibilities were found:
501 by Gary Gostin, 111 by others. 

October 05, 2020:
New largest known factor of a Fermat number
found:
 7 · 218233956 + 1  divides  F(18233954). 
The same prime also divides  GF(18233952,7), the largest
known composite  GF(m,a)  number for any basis  a ≤ 12.

July 06, 2020:
Summary of frequencies corrected and extended.

April 01, 2020:
Largest known divisor of a Generalized Fermat number
found:
 9 · 213334487 + 1  divides  GF(13334485,3),
GF(13334486,7)  and others.

February 11, 2020:
Gary Gostin starts generating new GFN divisibilities:
82 factors delivered at once.

February 10, 2020:
New factorization at GFNsmall.html:
Cofactor of  10^(2^8) + 3^(2^8)  is  P85 × P105.

January 22, 2020:
New factor of Fermat number F(5523858):
is new largest known factor of a Fermat number.

December 25, 2019:
Candidate of Extended Sierpinski Problem eliminated.

December 9, 2019:
New factor of Fermat number F(2587), which brings to 350
the total number of known factors.

October 16, 2019:
New factors of Generalized Fermat numbers GF(4800313,3)
and GF(4800310,5).

October 14, 2019:
New factor of Generalized Fermat number GF(4673541,7).

October 13, 2019:
New factor of Generalized Fermat number GF(4532462,11).

September 29, 2019:
New factor of Generalized Fermat number GF(3964696,11).

July 31, 2019:
Generalized Fermat number GF(25,10) proved composite.

July 6, 2019:
Generalized Fermat number GF(24,10) proved composite.

March 23, 2019:
New factor of Fermat number F(9863).

January 28, 2019:
New factor of Fermat number F(118).

December 31, 2018:
Table of factors GFNfacs.html now includes 6608
new divisibilities, 21 of them found in 2018.

December 19, 2018:
New factor of Fermat number F(132).

December 13, 2018:
New factor of Fermat number F(3345).

November 2, 2018:
New factor of Fermat number F(2144).

July 24, 2018:
New factor of Fermat number F(5199), which brings to 300
the total number of known composite Fermat numbers.

May 1, 2018:
New factor of Generalized Fermat number GF(10746,12).

April 5, 2018:
New factor of Fermat number F(274).

April 3, 2018:
Candidate of Extended Sierpinski Problem eliminated.

March 10, 2018:
New factor of Fermat number F(63480).

January 15, 2018:
New factorization at GFNsmall.html:
Cofactor of  11^(2^8) + 10^(2^8)  is  P62 × P107 .